Various antenna receiver systems have been designed in the past for determining either the transmitter direction or receiver position. For example, U.S. Pat. No. 2,861,264 to Lair relates to an antenna receiver system. The system is generally comprised of a single receiver antenna that not only includes rotary motion about its axis but also harmonic motion of the antenna between two points. The system also includes a comparator circuit for determining the direction and magnitude of the source at the receiver antenna location during its compound motion upon system use. U.S. Pat. No. 3,798,648 to Lammers discloses a double antenna direction finding system. The system is provided with one antenna being movable relative to and spaced from the other so as to obtain a frequency difference that can be converted into visual information. U.S. Pat. No. 4,042,929 to Dorey relates to a ground beacon navigation system for a helicopter. The system is provided with two antennas affixed to the outer ends of the rotary blade. An electronic signal processing circuit and display arrangement is connected to the antennas for processing the received beacon signals so as to indicate the spatial coordinate position of the helicopter. U.S. Pat. No. 4,060 809 to Baghdady discloses a system having at least one ground station for tracking an airborne moving object and for determining the position of the tracked object in spatial coordinates. The ground station system is generally comprised of a pair of orthogonally related antennas that are movable in relation to each other. These antennas function to radiate signals to and for receiving signals reflected from the object being tracked. The electronic components associated with the antennas transforms the received signals into visual information of azimuth, elevation and range of the object. However, none of the aforediscussed references, whether taken alone or in any combination, remotely suggest an improved method for continuously determining the orientation of a moving platform in relation to the earth by the use of a Global Positioning System (GPS) that is provided with a computerized GPS signal receiver apparatus which is mounted on the platform and which includes a single rotary antenna. The method includes, among other things, the steps of processing the GPS satellite signals received by the platform so as to continuously track an optimum group of four satellites despite the irregular and relatively low dynamic motions of the platform about and with respect to its axis as the platform moves along such axis (heading); and then transforming the signals of the tracked satellites received by a selected series of equidistant points about the antenna periphery into a graphic display of range data of each tracked satellite that can be interpolated at a selected and common time fix for enabling the mathematical determination of platform orientation thereat.